Fuzzy Linear Multi-Objective Stochastic Programming Models

2019 ◽  
pp. 78-127
Keyword(s):  
Deterministic Model ◽  
Programming Model ◽  
Probability Distributions ◽  
Ideal Point ◽  
Solution Process ◽  
Multi Objective ◽  
Fuzzy Goals ◽  
Objective Chance ◽  
Constrained Programming ◽  
The Individual

In this chapter, fuzzy goal programming (FGP) technique is presented to solve fuzzy multi-objective chance constrained programming (CCP) problems having parameters associated with the system constrains following different continuous probability distributions. Also, the parameters of the models are presented in the form of crisp numbers or fuzzy numbers (FNs) or fuzzy random variables (FRVs). In model formulation process, the imprecise probabilistic problem is converted into an equivalent fuzzy programming model by applying CCP methodology and the concept of cuts of FNs, successively. If the parameters of the objectives are in the form of FRVs then expectation model of the objectives are employed to remove the probabilistic nature from multiple objectives. Afterwards, considering the fuzzy nature of the parameters involved with the problem, the model is converted into an equivalent crisp model using two different approaches. The problem can either be decomposed on the basis of tolerance values of the parameters; alternatively, an equivalent deterministic model can be obtained by applying different defuzzification techniques of FNs. In the solution process, the individual optimal value of each objective is found in isolation to construct the fuzzy goals of the objectives. Then the fuzzy goals are transformed into membership goals on the basis of optimum values of each objective. Then priority-based FGP under different priority structures or weighted FGP is used for achievement of the highest membership degree to the extent possible to achieve the ideal point dependent solution in the decision-making context. Finally, several numerical examples considering different types of probability distributions and different forms of FNs are considered to illustrate the developed methodologies elaborately.

Methodology for Solving Multi-Objective Quadratic Programming Problems in a Fuzzy Stochastic Environment

2019 ◽  
pp. 177-217
Keyword(s):  
Quadratic Programming ◽  
Deterministic Model ◽  
Programming Model ◽  
Probability Distributions ◽  
Fuzzy Programming ◽  
Chance Constraints ◽  
Membership Functions ◽  
Quadratic Programming Problems ◽  
Constrained Programming ◽  
Fuzzy Programming Model

This chapter presents two methodologies for solving quadratic programming problems with multiple objectives under fuzzy stochastic environments. The right side parameters of the chance constraints of both the models are chosen as fuzzy random variables (FRVs) following different probability distributions. Like the previous chapters, chance constrained programming (CCP) methodology is employed to the fuzzy chance constraints to develop fuzzy programming model. In the first model, cut of fuzzy sets and fuzzy partial order relations are incorporated to the fuzzy programming model to develop an equivalent deterministic model. For the second model, defuzzification method of fuzzy numbers (FNs), which are presented in Chapter 2, are taken into consideration to generate equivalent quadratic programming model in a crisp environment. As the objective functions are quadratic in nature, it is easy to understand that the membership functions obtained through methodological development process are also quadratic in nature. To linearize the quadratic membership functions, linearization techniques are employed in this chapter. Finally, for achieving the maximum degree of each of the membership goals of the objectives, a fuzzy goal programming (FGP) approach is developed for the linearized membership goals and solved by minimizing under-deviational variables and satisfying modified system constraints in fuzzy stochastic decision-making environments. To illustrate the acceptability of the developed methodology presented in this chapter, some numerical examples are included.

A fuzzy multi-objective programming optimization model for emergency resource dispatching under equitable distribution principle

2021 ◽  
pp. 1-10
Author(s):  
Zhaoping Tang ◽  
Wenda Li ◽  
Shijun Yu ◽  
Jianping Sun
Keyword(s):  
Optimization Model ◽  
Programming Model ◽  
Ideal Point ◽  
Optimal Solution ◽  
Multi Objective ◽  
Emergency Rescue ◽  
Satisfaction Degree ◽  
Multi Objective Programming ◽  
Parameter Interval ◽  
Objective Programming

In the initial stage of emergency rescue for major railway emergencies, there may be insufficient emergency resources. In order to ensure that all the emergency demand points can be effectively and fairly rescued, considering the fuzzy properties of the parameters, such as the resource demand quantity, the dispatching time and the satisfaction degree, the railway emergency resources dispatching optimization model is studied, with multi- demand point, multi-depot, and multi-resource. Based on railway rescue features, it was proposed that the couple number of relief point - emergency point is the key to affect railway rescue cost and efficiency. Under the premise of the maximum satisfaction degree of quantity demanded at all emergency points, a multi-objective programming model is established by maximizing the satisfaction degree of dispatching time and the satisfaction degree of the couple number of relief point - emergency point. Combined with the ideal point method, a restrictive parameter interval method for optimal solution was designed, which can realize the quick seek of Pareto optimal solution. Furthermore, an example is given to verify the feasibility and effectiveness of the method.

Research on Feasible Direction Variation of Multi-Objective Genetic Algorithms and Simulation

2014 ◽  
Vol 644-650 ◽  
pp. 1965-1968
Author(s):  
Yue Li Li ◽  
Chao Wang
Keyword(s):  
Fitness Function ◽  
Ideal Point ◽  
Optimal Solution ◽  
Feasible Direction ◽  
Current Group ◽  
Multi Objective ◽  
Point Search ◽  
Solution Region ◽  
The Individual ◽  
The Ideal

The method provided in this paper can be according to the current population to readjust the weight, thus obtain toward the positive ideal point search pressure, finally converge to the optimal solution. This paper combines the feasible direction into genetic algorithm. This method can lead the individual to optimal solution region along feasible direction which approach the optimal solution sets. Through evaluating the degree of distance between chromosome and constrain, we introduce membership function into traditional GA and embed the information of infeasible solutions into fitness function. Propose a self-adapting evaluation function. This method can readjust the weights according to current group and then get the stress of searching to the ideal positive point. To a kind of fuzzy multi-objective optimization problem, propose a method of best satisfaction to transform the fuzzy models to clear ones and solve the models using GA based on interactive method. Then testify its validity though examples.

On Solving Multiobjective Transportation Problems With Fuzzy Random Supply and Demand Using Fuzzy Goal Programming

2018 ◽  
pp. 791-821
Author(s):  
Animesh Biswas ◽  
Nilkanta Modak
Keyword(s):  
Goal Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Optimal Solution ◽  
Fuzzy Goal Programming ◽  
Transportation Problems ◽  
Fuzzy Goal ◽  
Constrained Programming ◽  
The Individual ◽  
Fuzzy Random

In this article a fuzzy goal programming model is developed to solve multiobjective unbalanced transportation problems with fuzzy random parameters. In model formulation process the cost coefficients of the objectives are considered as fuzzy numbers and the supplies and demands are considered as fuzzy random variables with known fuzzy probability distribution from the view point of probabilistic as well as possibilistic uncertainties involved with the model. A fuzzy programming model is first constructed by applying chance constrained programming methodology in fuzzy environment. Then, the model is decomposed on the basis of the tolerance ranges of the fuzzy numbers associated with it. The individual optimal solution of each decomposed objectives is found in isolation to construct the membership goals of the objectives. Finally, priority based fuzzy goal programming technique is used to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing the under deviational variables and thereby obtaining optimal allocation of products by using distance function in a cost minimizing decision making environment. An illustrative example is solved and compared with existing technique to explore the potentiality of the proposed methodology.

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